Under positive scalar curvature and mean-convex boundary, a Morse index bound bounds area, genus, boundary components, and total curvature of free boundary minimal surfaces, while topology or area bounds alone fail to bound the others.
Free Boundary Minimal Surfaces in the Unit Three-Ball via Desingularization of the Critical Catenoid and the Equatorial Disk
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
We construct a new family of high genus examples of free boundary minimal surfaces in the Euclidean unit 3-ball by desingularizing the intersection of a coaxial pair of a critical catenoid and an equatorial disk. The surfaces are constructed by singular perturbation methods and have three boundary components. They are the free boundary analogue of the Costa-Hoffman-Meeks surfaces and the surfaces constructed by Kapouleas by desingularizing coaxial catenoids and planes. It is plausible that the minimal surfaces we constructed here are the same as the ones obtained recently by Ketover using the min-max method.
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math.DG 1years
2019 1verdicts
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Inequivalent complexity criteria for free boundary minimal surfaces
Under positive scalar curvature and mean-convex boundary, a Morse index bound bounds area, genus, boundary components, and total curvature of free boundary minimal surfaces, while topology or area bounds alone fail to bound the others.